The convergence space of minimal usco mappings

Details The convergence space of minimal usco mappings The convergence space of minimal usco mappings

2006-08-03

arxiv.org/abs/math/0608086v1

Mathematics

General Topology

32 pages

Scientific paper

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed.

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